Higher spin theory

TL;DR

This paper reviews classical higher spin gauge theories in flat spacetime, highlighting formalism, formulations, and recent computational verifications, aiming to unify and clarify the theoretical framework.

Contribution

It provides a comprehensive review of unconstrained formulations of free and coupled higher spin theories, correcting previous errors and exploring a potential unified equation of motion.

Findings

Confirmed results for non-local unconstrained formulations

Corrected previous calculational errors

Provided computer-assisted calculations and code

Abstract

We provide a review of gauge field theories with higher spin, focusing on the classical theory of massless bosons in flat Minkowski spacetime. A brief introduction to the concept of spin is provided along with a historical review of some of the most important problems and accomplishments in higher spin theory, followed by a review of familiar lower spin theories. Using a particularly elegant formalism, we examine the free higher spin theory and the theory coupled to a generic external current. For both of these theories, we review their constrained and the unconstrained formulation, focusing our attention on the latter. We also review the existing literature, confirming the results for the non-local unconstrained formulation and correcting some calculational errors. We briefly discuss the geometrical motivation behind the construction of the basic building blocks of the theory and we entertain the possibility of there being a single equation of motion for all bosonic higher spin fields. Some explicit calculations obtained using computer-assisted methods are provided in the appendix, along with the relevant computer code.